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LEDs, viewing angle, and power density

I was reading the spec sheet on a particular LED and noticed that the viewing angle (2*Θ½) is specified as 30 degrees min and 60 degrees max.

This got me wondering, if I had LEDs with 30 and 60 degree viewing angles, put the same current through them both, will the light emitted from the 60 degree LED have a lower power density?

It seems like it would be lower for the 60 degree LED since the same amount of light is spread out over a greater area, but maybe I am missing something.
 

(*steve*)

¡sǝpodᴉʇuɐ ǝɥʇ ɹɐǝɥd
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The light output of a LED typically is greatest on axis and drops as you move off axis.

Frequently they quote the angle at which the intensity falls to 1/2 the on-axis intensity.

This doesn't mean the LED is invisible beyond this point, but it may very rapidly get dimmer.

Note that there are some lens configurations which give almost zero on axis intensity, and max at 90 degrees, so not all LEDs perform the way I have noted above. The behaviour is pretty much a property of the lens.

Yes, all other things being equal, a LED with a smaller half angle will appear brighter (on axis) since the same amount of light is spread over a smaller angle. Equally, it will appear dimmer when you are considerably off axis because the light intensity will fall off faster.

Does that answer the question?
 
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